Macroscopic Coherence and Effective Sources in Relative-Entropy Semiclassical Gravity

Relative-entropy derivations of gravity require specifying a macroscopic source algebra. We propose that, for neutral matter, the relevant object is the Araki--Uhlmann relative entropy of states restricted to the C-even stress-energy carrier algebra, separating gravitational sourcing from C-odd electromagnetic readout. For superconducting condensates, we model the C-even source-state dependence by a susceptibility of order $\alpha\Delta/E_F$, identifying London-moment measurements as a ppm-scale constraint channel.